This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
The production of hydrocarbons, such as oil and gas, has been performed for numerous years. To produce these hydrocarbons, geophysical data about specific areas is obtained to provide a model of subsurface reservoirs via computer systems, such as simulators. As can be appreciated, the technology utilized to obtain this geophysical data has been applied for onshore mineral exploration, oceanic tectonic studies, and offshore petroleum and mineral resource exploration. Based on the models, a wellbore may be drilled to the subsurface reservoir and devices may be placed into the wellbore to access the formation fluids. These formation fluids may flow through the wellbore to surface facilities for further processing.
Reservoir connectivity, which is a measure of the ability of fluid to communicate between any points or regions within a reservoir, is one of the primary factors that controls hydrocarbon production efficiency and ultimate recovery. Despite efforts by geoscientists and engineers, measuring and quantifying connectivity in geologic or reservoir models is still a challenge in reservoir characterization and modeling. There are generally at least five components utilized to measure reservoir connectivity. First, reservoir connectivity should be measured not only between two points (local), but also for the entire geologic/reservoir model (global). Second, reservoir connectivity measures should reflect “effective connectivity” resulting from different reservoir recovery processes. Third, reservoir connectivity measures should be scale/grid-independent. Fourth, reservoir connectivity measures calculations should be computationally efficient. Fifth, the method to estimate reservoir connectivity measures should result in minimum errors.
Typically, current technologies in reservoir connectivity measures in geologic/reservoir models may be divided into two groups, which are flow simulation based and flow property based. Flow simulation based approaches use a full flow simulator that solves the complex physical differential equations to simulate reservoir performance and its performance responses (e.g., velocity, productivity, and sweep efficiency). See Malik, Z. A. et al., “An Integrated Approach to Characterize Low-Permeability Reservoir Connectivity for Optimal Waterflood Infill Drilling,” SPE 25853 (1993); and Gajraj, A. et al., “Connectivity-Constrained Upscaling,” SPE 38743 (1997). Reservoir connectivity may be estimated and evaluated using the full flow simulation results. However, because this approach is computationally intensive, only small models (a model with less than one million cells) may be reasonably analyzed for a few points in the reservoir model rather than the entire reservoir model. As such, the flow simulation based approach is too computationally expensive for reservoir connectivity studies when a geologic model is composed of ten million cells or more, which is common in reservoir characterization and modeling applications.
The flow property based approach may also include different methods to perform a connectivity calculation. For instance, the flow property based approach may include the potential propagation method, the resistivity index method, the least resistance method, and the fast marching method. The potential propagation method uses a “wave front” driven by “potential” (i.e. the breadth-first search (BFS) method) to search the shortest distance between two given points. See Alabert, F. G. et al., “Stochastic Models of Reservoir Heterogeneity: Impact on Connectivity and Average Permeabilities,” SPE 24893 (1992); and Petit, F. M. et al., “Early Quantification of Hydrocarbon in Place Through Geostatistic Object Modelling and Connectivity Computations,” SPE 28416 (1994). In this method, flow properties (e.g. horizontal and vertical permeabilities) are used as thresholds to turn a geologic/reservoir model into binary codes (e.g. 1 for flow and 0 for no flow), and reservoir connectivity is analyzed using these binary codes. However, the use of the thresholds only introduces possible errors because the heterogeneity of the flow properties is not taken into account. In addition, the shortest distance search method introduces large orientation errors (i.e. up to about 29.3%), which are the result of the geometry of the cells or grid blocks utilized in the model. As such, the potential propagation method is not accurate because it does not account for reservoir heterogeneity and creates large orientation errors in the shortest distance search.
The resistivity index method uses a resistivity index to replace the binary codes in the potential propagation method. See Ballin, P. R. et al., “New Reservoir Dynamic Connectivity Measurement for Efficient Well Placement Strategy Analysis Under Depletion,” SPE 77375 (2002); and Hird, K. B. et al., “Quantification of Reservoir Connectivity for Reservoir Description Applications,” SPE Reservoir Evaluation & Engineering pp. 12-17 (February 1998). The use of fluid flow properties (e.g. transmissibility) in the resistivity index method improves the potential propagation method over methods that utilize the thresholds. However, this method is grid/scale-dependent because it uses transmissibility as a search weight (or cost function). The grid/scale-dependence makes comparing models with different grids/scales impossible or difficult because the different grids/scales are not comparable. Further, this method still has the orientation errors in the shortest distance search, which are similar to the potential propagation method.
The least resistance method is similar to the resistivity index method except that the least resistance method uses a different mechanism, such as the graph theory, to determine the shortest path. See Hirsch, L. M. et al., “Graph theory applications to continuity and ranking in geologic models,” Computers & Geoscience 25, pp. 127-139 (1999); and International Patent Application No. PCT/US04/32942. This method, which is similar to the resistivity index method, is grid/scale-dependent, which makes comparing models with different grids/scales difficult. Further, while the use of unstructured grids may reduce the errors to 13.4%, these orientation errors are still present in this method.
Finally, the fast marching method enhances the previous methods by reducing the orientation errors from more than 10% in the resistivity index method and the least resistance method to less than 1%. See Richardsen, S. K. et al., “Mapping 3D Geo-Bodies Based on Level Set and Marching Methods,” Mathematical Methods and Modeling in Hydrocarbon Exploration and Production, edited by Iske, A. and Randen, T., Springer-Verlag, Berlin pp. 247-265 (2005); and Sethian, J. A., “Fast Marching Methods,” SIAM REVIEW, Vol. 41, No. 2, pp. 199-235 (1999); and International Patent Application Publication No. WO2006/127151. Similar to the other existing methods, the fast marching method is developed to quantify reservoir connectivity between two points or from one given point to any other points rather than addressing the global connectivity for the entire geologic/reservoir model. In particular, this method has been used primarily in seismic-based connectivity modeling. As such, the fast marching method is a local method that is difficult to use for anisotropic problems and utilizes a velocity field that is assumed because it is generally not available.
While these typical methods may be utilized, these methods fail to address each of the components mentioned above. As such, the need exists for a method of measuring reservoir connectivity that addresses these requirements.
Other related material may be found in at least U.S. Pat. No. 6,823,266 and U.S. Patent Publication No. 20040236511. Further, related information may be found at least in Lin, Q., “Enhancement, Extraction, and Visualization of 3D Volume Data,” Ph. D. Dissertation, Institute of Technology, Linkoping University, Linkoping, Sweden, (April 2003); McKay, M. D. et al., “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, Vol. 21, No. 2, pp. 239-245, (May 1979); and Pardalos, P. M. and Resende, M. G. C. (Edited), Handbook of Applied Optimization, Oxford University Press pp. 375-385 (2002).